Find the area of the shaded region. Round your answer to the nearest hundredth.

12=side length

The area of the shaded region is about — square units.

How do you find the area of the shaded region? Thank you!

Find The Area Of The Shaded Region. Round Your Answer To The Nearest Hundredth.12=side LengthThe Area

Answers

Answer 1

Answer:

Step-by-step explanation:

Divide 360 by the number of sides in a regular polygon to find θ

θ = 360/5 = 72°

Use law of cosines to find the radius of the circle which equals the common length sides of the isosceles triangle

12² = R² + R² - 2•R•Rcos72

12² = 2R² - 2R²cos72

12² =  2R²(1 - cos72)

R² = 12² / 2(1 - cos72)

R² = 104.1993788...

R = 10.2078...

The height of the isosceles triangle is

h = Rcos(θ/2) = 10.2078cos(72/2) = 8.258291...

The shaded area is the area of the circle minus the area of the pentagon.

A = π(104.1993) - 5(½(12)(8.258291))

A = 327.35200... - 247.74874...

A = 79.6032575...

A = 79.60 units²

Find The Area Of The Shaded Region. Round Your Answer To The Nearest Hundredth.12=side LengthThe Area
Answer 2

The Area of the shaded region is A = 79.60 units²

What is law of Cosine?

A planar triangle's side's square is equal to the sum of the squares of the other sides minus the product of those sides and the cosine of the angle that separates them by two.

Given:

length= 12

So, Divide 360 by the number of sides in a regular polygon

θ = 360/5

θ = 72°

Use law of cosines

12² = R² + R² - 2 x R x Rcos72

12² = 2R² - 2R² cos72

12² =  2R²(1 - cos72)

R² = 12² / 2(1 - cos72)

R² = 104.1993788...

R = 10.2078...

Thus, the height of the isosceles triangle is

h = R cos(θ/2)

   = 10.2078cos(72/2)

   = 8.258291...

and, the shaded area is

A = π(104.1993) - 5(½)(12)(8.258291))

A = 327.35200 - 247.74874

A = 79.6032575

A = 79.60 units²

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Related Questions

Hello can someone please help me with this

Answers

Answer:

I would assume it is c. 1, because of rounding, but I'm only 70% sure.

Craig has a job waiting tables where he earns $3.45 per hour plus tips. Craig earned $73.68 in tips during his shift yesterday.

If x represents the number of hours Craig worked yesterday, which of the following equations can be used to find the amount of money Craig earned yesterday?
A. y = 3.45x - 73.68
B. y = 73.68x + 3.45
C. y = 3.45x + 73.68
D. y = 73.68x - 3.45

Answers

C is the right answer

Michael paid an entrance fee of $8 plus an additional $2.25 per game at the bowling alley. He spent $50.00. Write and solve an equation to determine how many games Michael played.

Answers

Answer:

4

Step-by-step explanation:

$8.00+$2.25 = $10.25

$50.00÷$10.25= 4.

Give the digits in the hundred thousands place and the ten thousands place.
746,089

Answers

Answer:

Hundred thousands - 7

Ten Thousands- 4

Step-by-step explanation:

Fdgbfrgrth Rheu Hyueheuhuhuhuheeuhuhuhe

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Shajananbe be bf NBC Judah’s

The circle graph shows a family budgets it’s annual income.if the total annual income is 140,000, what amount is budgeted for auto expenses?

Answers

Answer: The amount budgeted for Auto Expenses is $18,200

Step-by-step explanation:

13 Percent of $140,000 is $18,200

0.13 times 140,000 :-)

Please answer right!

Answers

Answer:

Step-by-step explanation:

5x + 2 - 3x - 1 = 3x + 2

5x - 3x - 3x = - 2 + 1 + 2

5x - 6x = 1

-1x = 1

x = 1 / -1

x = -1

3x-1 over 5 = x+1 over 3

I need asap

Answers

Answer:

(3x-1)/5= (x+1)/3

3(3x-1)=5(x+1)

then solve which the final answer will give you x=8

What equals 10³ I need to know

Answers

Answer:

1,000

Step-by-step explanation:

10 x 10 x 10 = 1,000

1000

Step-by-step explanation:

10³

=10×10×10

1000

I need to know that answer please help if you can

Answers

Answer:

$180

Step-by-step explanation:

y = 30x +150

30(1) + 150

= 180

Which of the following is not a solution of the equation below (3x(x-1)(x-2)=0

Answers

What is the options?

solve the equation and justify each step using the algebraic properties of equality

Answers

Answer:

-5

Step-by-step explanation:

3x=-13-2

3x=-15

x=-5

plz plz heelp me i need heelp

Answers

C because 1.04 could be rounded to 1 to the nearest whole number

Write $1.50 to $12.00 as a ratio in fraction form in lowest terms.

Answers

Answer:

1/8

Step-by-step explanation:

Refer to the map shown in exercise.2. If m.angle 1 os 64° what is the measure of angle.2?

Answers

post the map
we need to see α photo in order to answer the question.

Answer:180

Step-by-step explanation:

Question 5 - Last night 20 mm of rain fell in 4 h. If it continues raining at the same rate, how
long will it take for 45 cm of rain to fall?

Answers

Answer:

Step-by-step explanation:

45 divided by two

Angles 1 and 2 are coresponding angles angle 1 is 3x+15 angle 2 is 4x-5 degrees.
what is the value of x

Answers

Answer:

10

Step-by-step explanation:

3x+15+4x-5=180

7x+10=180

7x=170

x=10

Pleased help math experts urgent

Answers

Answer:

1. get closer to 0

2. symmetrical across y=-x

3. x cannot be equal to 0

4. decreasing if x<0, increasing if x>0

Step-by-step explanation:

yes

The lcm of 5^3 and 5^2 is?

Answers

Answer:

Step-by-step explanation:

5³ is the answer since it's the greater between the two numbers

Answer:

125

Step-by-step explanation:

This is because 5^2 *5 is 125 and 5^3 * 1 = 125   and the findings are both numbers have to be multiplied by a whole number to quantify a same identical multiple total number - we can check this by dividing by the smallest 125/5^2  = 5  and then the largest is 125/5^3 = 1 and we know there could not be a smaller whole number  - The other workings would be to do a prim e factor tree   of 125  =  5  25  5 and 5 =  5^3 and here we are told 5^3 is a multiple of 125 and 5^2 is also a multiple of 5^3 as it square fits 5 times into 125 as 5*25 is 125  

6x+3>15 solve for a please

Answers

Answer:

x>2

Step-by-step explanation:

1) 6x+3 > 15

2) 6x > 15-3

3) 6x > 12

4) x > 12÷6

5) x > 2

Please help me with this question. What formula would you use to find the missing lengths of the right triangles?

Answers

a2 + b2 = c2 can be use to find missing lengths of the right triangles

If 20% of the students were boys, what fraction were girls?

Answers

Answer:

Girls are   4/5 of the students.

Step-by-step explanation:

boys + girls = 100% of students.

If 20% of the students are boys then 80% are girls

80% = 80/100 =  4/5

For a project in his Geometry class, Ryan uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 12.15 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. He then walks 3.4 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.35 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

Answers

9514 1404 393

Answer:

  4.82 m

Step-by-step explanation:

The mirror reflects light at the same angle the light hits it, so the triangles formed by the line of sight, the ground, and the objects involved are similar. This means corresponding lengths are proportional.

  height/mirror distance = T/12.15 = 1.35/3.4

Multiplying by 12.15, we find the top of the goalpost to have a height of ...

  T = 12.15(1.35/3.4) ≈ 4.82 . . . meters

The goalpost is about 4.82 meters high.

Angle ABC And BCA a are complementary angle ABC is 85° if angle BCA is named as 3b -7 what could be the value of b?

Answers

Complementary angles add to 90 degrees

Therefore,

angle ABC + angle BCA = 90

But, angle BCA = 3b - 7

and angle ABC = 85

Therefore,

85 + 3b - 7 = 90

3b - 7 = 5

3b = 12

b = 4

Solve the inequality 10y−3(y+2)>2y+4, and write the solution in interval notation.

Answers

Step-by-step explanation:

10y - 3(y + 2) > 2y + 4

10y - 3y - 6 > 2y + 4

(10 - 3 - 2)y > 4 + 6

5y > 10

y > 10/5

y > 2

[tex] \: [/tex]

Solution → y > 2

Interval Notation → [tex] \lang 2 , \infty\rang[/tex]

The solution in interval notation is: (2, ∞)

To solve the inequality 10y - 3(y + 2) > 2y + 4, follow these steps:

Step 1: Distribute the -3 on the left side of the inequality:

10y - 3y - 6 > 2y + 4

Step 2: Combine like terms:

(10y - 3y) - 6 > 2y + 4

7y - 6 > 2y + 4

Step 3: Get all the y terms on one side by subtracting 2y from both sides of the inequality:

7y - 2y - 6 > 2y - 2y + 4

5y - 6 > 4

Step 4: Get the constant term on the other side by adding 6 to both sides of the inequality:

5y - 6 + 6 > 4 + 6

5y > 10

Step 5: Finally, solve for y by dividing both sides by 5:

y > 10/5

y > 2

The solution to the inequality is y > 2. Now, let's write it in interval notation.

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Third question please need help

Answers

Answer:

add 6 time 8 and get the answer like that.

Step-by-step explanation:

just keep adding that what you need to do ok.

(b) Notice that x=0.5 meter when θ = 45o. By approximately how many radians should you increase θ if you want the x coordinate of the point R to decrease to x = 0.45 meters? Use the tangent line approximation.

Answers

The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].

Based on the statement we construct the geometric diagram, by definition of tangent we have expressions for the initial and final angles ([tex]\theta_{1}[/tex], [tex]\theta_{2}[/tex]), in radians, of the figure:

Initial triangle

[tex]\tan \theta_{1} = \frac{y_{1}}{x_{1}}[/tex] (1)

Final triangle

[tex]\tan \theta_{2} = \frac{y_{2}}{x_{2}}[/tex] (2)

By using (2), the equivalence [tex]\theta_{2} = \theta_{1}+\Delta \theta[/tex] and trigonometric identities we have the following expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\tan \theta_{1}+\tan \theta_{2}}{1-\tan \theta_{1}\cdot \tan \theta_{2}}[/tex] (3)

By (1), we simplify the expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}} + \tan \Delta \theta}{1-\frac{y_{1}}{x_{1}}\cdot \tan \Delta \theta}[/tex] (3b)

If [tex]0 \le \Delta \theta \le \frac{\pi}{6}[/tex], then we can use the following approximation:

[tex]\tan \Delta\theta \approx \Delta \theta[/tex] (4)

Then, we reduce (3b) into an entirely algebraic expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}}+\Delta \theta }{1-\frac{y_{1}}{x_{1}}\cdot \Delta \theta }[/tex] (3c)

Where [tex]y_{2} = \sqrt{r^{2}-x_{2}^{2}}[/tex].

Now we clear [tex]\Delta \theta[/tex] within the formula:

[tex]\Delta \theta = \frac{\frac{y_{2}}{x_{2}}-\frac{y_{1}}{x_{1}}}{\frac{y_{1}}{x_{1}}\cdot \left(1+\frac{y_{2}}{x_{2}} \right) }[/tex]  (5)

If we know that [tex]x_{1} = y_{1} = 0.5[/tex], [tex]r = 0.707[/tex] and [tex]x_{2} = 0.45[/tex], then we estimate the angle change:

[tex]y_{2} = \sqrt{0.707^{2}-0.45^{2}}[/tex]

[tex]y_{2} \approx 0.545[/tex]

[tex]\Delta \theta = \frac{\frac{0.545}{0.45}-1 }{1\cdot \left(1+\frac{0.545}{0.45} \right)}[/tex]

[tex]\Delta \theta = 0.095[/tex]

As [tex]\Delta \theta < \frac{\pi}{6}[/tex], then the result seems to be reasonable. The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].

We kindly invite to check this question on trigonometric identities: https://brainly.com/question/24836845

Jack bought a 1/4 pound of salami and 1 2/3 pounds of Ham at the deli. Both items are on sale for $12 per pound. What is the total cost?

Answers

Answer:

Salami: $3.00

Ham: $ 8.00

Step-by-step explanation:

12 * 1/4 = 12/4 = $3.00

12 * 2/3 = 24/3 = $8.00

*What is the correct value of b?
~50/100 = b/28
-b=14
-b=20
-b=10
*What is the value of n?
~25/100 = 7/n
-n=28
-n=24
-n=32

Answers

Answer:

-b = 14

-n = 28

Step-by-step explanation:

For b

50/100=b/28 cross-multiply

1400= 100b divide both sides by hundred

-b = 14

For n

25/100= 7/n cross multiply

25n = 700 divide both sides by 25

-n = 28

Log2(x-1)+Log2(x+2) =2
Find X

Answers

X is 2.82 rounded off :)
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